Number of lone pair (s) of electrons on central atom and the shape of \(BrF _{3}\) molecule respectively, are ..... .

The surface of sodium metal is irradiated with radiation of wavelength \(x\) nm. The kinetic energy of ejected electrons is \(2.8 \times 10^{-20}\) J. The work function of sodium is \(2.3\) eV. The value of \(x\) is _____ \(\times 10^2\) nm. (Nearest integer)
(Given: \(h = 6.6 \times 10^{-34}\) J s; \(1\) eV \(= 1.6 \times 10^{-19}\) J; \(c = 3.0 \times 10^8\) m s\(^{-1}\))

The equilibrium constant at \(298\, K\) for a reaction \(A + B \rightleftharpoons C + D\) is \(100.\) If the initial concentration of all the four species were \(1\, M\) each, then equilibrium concentration of \(D\) ( in \(mol\, L^{-1}\) ) will be :

Consider the complex ions, \(trans-[Co(en)\left._{2} Cl _{2}\right]^{+}( A )\) and \(cis-[Co(en)\) \(\left._{2} Cl _{2}\right]^{+}\) \((B).\) The correct statement regarding them is :

The order of reactivity of the given haloalkanes towards nucleophile is

Given below are two statements: Statement \(I : C _{2} H _{5} OH\) and \(AgCN\) both can generate nucleophile. Statement \(II : KCN\) and \(AgCN\) both will generate nitrile nucleophile with all reaction conditions. Choose the most appropriate option :

Which of the following tests cannot be used for identifying amino acids?

For \(\mathrm{n} \geq 2\), let \(S_n\) denote the set of all subsets of \(\{1,2 \ldots . . ., n\}\) with no two consecutive numbers. For example \(\{1,3,5\} \in \mathrm{S}_6\), but \(\{1,2,4\} \notin \mathrm{S}_6\). Then \(n\left(\mathrm{~S}_5\right)\) is equal to ________

move in opposite direction with speed ratio \(1: 2\). The following figure represents two biconvex lenses \(L_1\) and \(L_2\) having focal length \(10 \mathrm{~cm}\) and \(15 \mathrm{~cm}\) respectively. The distance between \(\mathrm{L}_1 \& \mathrm{~L}_2\) is _______.

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is \(12\,cm\). when viewed from the opposite side, the apparent distance of the bubble is observed as \(4\,cm\). If the side of the ice cube is \(24\,cm\), the refractive index of the ice cube is \(.....\).

\(X Y\) is the membrane / partition between two chambers 1 and 2 containing sugar solutions of concentration \(c_1\) and \(c_2\left(c_1 \gt c_2\right) \mathrm{mol} \mathrm{L}^{-1}\). For the reverse osmosis to take place identify the correct condition
(Here \(p_1\) and \(p_2\) are pressures applied on chamber 1 and 2)

(A) Membrane/Partition; Cellophane, \(\mathrm{p}_1 \gt \pi\)
(B) Membrane/Partition ; Porous. \(\mathrm{p}_2 \gt \pi\)
(C) Membrane/Partition ; Parchment paper, \(\mathrm{p}_1 \gt \pi\)
(D) Membrane/Partition : Cellophane, \(\mathrm{p}_2 \gt \pi\)
Choose the correct answer from the option given below :

A line drawn through the point \(P(4, 7)\) cuts the circle \(x^2 + y^2\, = 9\) at the points \(A\) and \(B\). Then \(PA· PB\) is equal to

A diatomic molecule has a dipole moment of \(1.2 D\). If the bond distance is \(1 \mathring A\), then fractional charge on each atom is _______ \(\times 10^{-1}\) esu. (Given \(1 \mathrm{D}=10^{-18}\) esu \(\mathrm{cm}\) )